What two things does Jane learn at Moor House (other than her inheritance)?

The chapters you want to focus on are 33 and 35 to answer
this question. Chapter 33 details how St. John one snowy night comes to Jane´s school
house and tells her about her uncle dying and then the inheritance she has received. He
also tells her how she and St. John and his sisters are related - they are cousins. This
chapter is also when Jane realises that St. John knows who she really is and her past
relations with Rochester. Take note of how important the realisation that Jane has
family is to her. After many chapters of thinking she was in the world by herself,
finally she has family that she can call her own, and this is of far more worth than
money:

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Glorious discovery to a lonely wretch! This was
wealth indeed! - wealth to the heart! - a mine of pure, genial affection. This was a
blessing, bright, vivid, and exhilarating - not like the ponderous gift of gold: rich
and welcome enough in its way, but sobering from its
weight.

To Jane, this
discovery is of far more importance than her inheritance, and marks her rise, not just
in terms of wealth, but also in terms of connections - a vital aspect of life in
Victorian society. Note how it is described as though it were gold, but not "sobering in
its weight".

Chapter 34 and 35 marks the discovery that her
cousin St. John wants to marry her - but not for love, only so he can have a suitable
work-mate to help him with his missionary work. Jane finally finds the strength to
refuse him and at the end of the Chapter she "hears" Rochester´s voice calling to her,
which is very important as it gives her the strength to break free from the constricting
relationship with St. John and leave to find Rochester. Note how Jane ends this
chapter:

I
broke from St. John; who had followed, and would have detained me. It was
my time to assume ascendancy. My powers were
in play, and in force.

This
is the knowledge or the "push" that Jane needs to assert herself and her own will to
live her own life rather than being pushed into living the life others would have her
live.